Sensitivity studies of high-precision methane column concentration inversion using a line-by-line radiative transfer model

Abstract

Hyper-spectral remote sensing may provide anβeffective solutionβto retrieve the methane (CH₄) concentration in an atmospheric column. As a result of exploringβthe absorptive characteristics of CH₄,βan appropriate band is selected from hyperspectral data for the detection ofβitsβcolumn concentration with high precision. Following the most recent inversion theory and methods, the line-by-line radiative transfer model (LBLRTM) is employed to forward model the impact of four sensitive factors on inversion precision, including CH₄ initial profile, temperature, overlapping gases, and surface albedo. The results indicate that the four optimized factors could improve the inversion precision of atmospheric CH₄ column concentration.

Keywords

methane / inversion / radiance / sensitivity / forward model / high precision

Introduction

Methane (CH₄) is the most abundant hydrocarbon in the atmosphere, which is also one of the most important atmospheric greenhouse gases (CO₂, CH₄, NO₂, O₃, HFCs, PFCs, SF₆) affected by anthropogenic activities (de Chazournes, 1998).The contribution of atmospheric CH4 to the warming climate is increasing, its radiance forcing is 0.48w/m² , which is approximately 18% of the overall radiative forcing caused by long-lived greenhouse gases (LLGHGs) (Khalil and Rasmussen, 1984), this makes CH₄ the second most important LLGHG. Approximately 40% of the atmospheric CH₄ comes from natural ecosystems i.e. wetlands and termites. On the other hand,the left share are mainly caused by anthropogenic activities, i.e., ruminants, rice agriculture, fossil fuel exploitation, landfills and biomass burning. The CH₄ concentration was 1.808 ppmv in 2010, an increase up to 0.28% compared with that in 2009, and 258% compared with that in 1750 (Barrie et al., 2011). Although the atmospheric CH₄ concentration is far less than that of carbon dioxide (CO₂), whereas its greenhouse effect ( unit concentration) is 25 times stronger than that of CO₂ ( Forster et al., 2007). The continual growth of the atmospheric CH₄ concentration will affect the Earth’s radiation balance and thus directly influence climate change (Parker et al., 2011).

CH₄ is also an important chemical in terms of active carbon composition. Its chemical effect in the troposphere affects the concentrations of hydroxyl radicals (OH) and carbon monoxide (CO) (Etheridge et al., 1992; Grutzen, 1995). The chemistry of CH₄ plays an important role in determining the chemical composition of atmosphere and indirectly affects climate and the environment, which in turn impacts human survival. Approximately 85% of CH₄ molecules emitted to the atmosphere are removed by oxidation (Bergamaschi et al., 2005; Frankenberg et al., 2011). This process is initiated by reaction with the hydroxyl radical (OH) (Dlugokencky et al., 1994; Qin and Zhao, 2003):

\mathrm{C}\mathrm{H}\mathrm{4}+\mathrm{O}\mathrm{H}\to \mathrm{C}{\mathrm{H}}_{\mathrm{3}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}

\mathrm{C}{\mathrm{H}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}+\mathrm{M}\to \mathrm{C}{\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}+\mathrm{M}

\mathrm{C}{\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}+\mathrm{3}{\mathrm{O}}_{\mathrm{2}}+\mathrm{M}\to \mathrm{C}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{O}\mathrm{H}+\mathrm{2}{\mathrm{O}}_{\mathrm{3}}

\mathrm{C}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{4}{\mathrm{O}}_{\mathrm{2}}+\mathrm{2}h\nu \to \mathrm{C}\mathrm{O}+\mathrm{2}\mathrm{O}\mathrm{H}+\mathrm{2}{\mathrm{O}}_{\mathrm{3}}

\mathrm{C}\mathrm{O}+\mathrm{2}{\mathrm{O}}_{\mathrm{2}}+h\nu \to \mathrm{C}{\mathrm{O}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}

CH₄ oxidation eventually produces CO₂ and may also yield ozone (O₃) under conditions where the nitric oxide mixing ratio exceeds 5 to 10 ppt (parts per trillion, where 1 trillion= 10¹², by volume) (Dlugokencky et al., 1994). The impact of CH₄ on climate change probably goes beyond the previous estimates.

However, researches about CH₄ are limited. Intermittent, few field observations of CH₄ could be dated back to the 1960s, and systematic research on CH₄ did not begin until the 1980's (Zhou and Li, 1990). Satellite remote sensing had been widely used to monitor the CH₄ sink/source dynamics and its variations over the past 10 years. Compared with the near-surface observations, this method can provide stable, long-term information with good spatial-temporal consistency at the regional and even global scale.

The observed data indicate that increasing atmospheric temperature is closely related to increasing greenhouse gas emissions over the past 100 years (IPCC 2007). However, the correlation between greenhouse gases and global warming is still not totally understood, due to the limited information about greenhouse gas sources /sinks. As a first procedure to answer the question mentioned above, the realization of high-precision detection of global CH₄ is crucial for assessing future global warming trends. The high sensitivity and resolution data will help improve the inversion precision of CH₄ column concentration by considering factors such as initial profile, temperature, interference of overlapping gas absorption, and surface albedo.

Different techniques have recently been used to understand the sensitivity of CO₂. Mao and Kawa (2004) had discussed the sensitivity studies of space-based measurements of atmospheric total column CO2 by reflected sunlight. Dai and Shi (2008) had reviewed studies with respect to the atmospheric CO₂ concentration from FengYun- 3 satellite (FY-3). On the other hand, Ye et al. (2011) had recently reported the sensitivity of retrieval of atmospheric column CO₂ was high. However, few studies were reportedβaboutββtheβsensitivityβofβatmosphericβCH₄βretrieval in theory and also its application.

This paper first describes the basic absorptive features of the 7.66 μm band for a realistic atmosphere with absorption. The dependence of the radiance sensitivity on the CH₄ initial profile, temperature, overlapping gases, and surface albedo are also addressed. This study focuses on the response of the back-to-space radiances in the 7.66 μm band to the variations of atmospheric CH₄ in the boundary layer and other variables. The previous studies are extended through examining the spectral sensitivity of the detected radiances over varying set of atmospheric conditions in greater detail using the line-by-line radiative transfer model (LBLRTM<FootNote>

http://rtweb.aer.com/lblrtm.html

</FootNote>). The key question is to determine the effect of four sensitive factors (i.e., CH₄ initial profile, temperature, overlapping gases, and surface albedo) on inversion precision. Although specific instrumentation or instrument characteristics are not included, the results of this study may provide a potential solution for the development of future forward models and a precise inversion algorithm.

CH₄ absorption

Absorption characteristics of atmospheric molecules

Solar radiation is absorbed, reflected, refracted, and scattered when passing through the atmosphere. The attenuation extent differs by electromagnetic wave bands. Atmospheric absorption refers to the radiation which is reflected back into space when sunlight passes through the atmosphere to the ground. Atmospheric molecules have many infrared absorption bands. The sunlight carries information about the abundance of atmospheric molecules when it passes through the atmosphere, from which it can be obtained from the total absorbing gas content and the vertical distribution. H₂O, CO₂, and O₃ are the main gases contributed to the solar radiation absorption.

Absorption spectrum

Generally, the band for the inversion of gas concentration should have strong radiative intensity to achieve signal detection with a high signal-to-noise ratio. However, the strength of gas absorption was moderate in this study: if it is too weak, it will not be sensitive to change in concentration; In contrast, if it is too strong, it will saturate the detector easily. In this study, the band of 1200-1400 cm^-1 is chosen from the HITRAN (high-resolution transmission molecular absorption) 2008 database Rothman et al. (2009) to invert. In the atmosphere, the approximate total vertical column contents are as follows: CH₄, 3.4×10¹⁹ molecules/cm²; H₂O, 4.6×10²² molecules/cm²; O₃, 6.8×10¹⁸ molecules/cm²; N₂O, 6.0×10¹⁸ molecules/cm²; CO, 1.8×10¹⁸ molecules/cm² (Shi, 2007). Considering the content of these gas molecules in the atmosphere, the LBLRTM is used to model the atmospheric transmissivity assuming that each of the above gas molecules exists alone (atmospheric conditions using the U.S. standard atmosphere). As shown in Fig.1, the main interferences for CH₄ inversion are H₂O and N₂O in the band of 1200-1400 cm^-1.

Inversion theory

Inversion band

The main principles for the selection of the inversion bands for the target gas are with high sensitivity and minimal interference by other absorptive gases. Covered by Infrared Atmospheric Sounding Interferometer (IASI<FootNote>

http://smsc.cnes.fr/IASI/GPsatellite.htm

</FootNote>) (Blumsteina et al., 2004; Masiello et al., 2009), the infrared absorption band at 7.6 μm can be used for CH₄ inversion, for which the main overlapping absorptive gases are H₂O and N₂O. The interference of N₂O is primarily in the band of 1250-1320 cm^-1, whereas H₂O influences the whole band. As the inversion of H₂O can be realized from other infrared or microwave bands, the band of 1320-1360 cm^-1 is selected.

Inversion theory

In the plane-parallel atmosphere with local thermodynamic equilibrium, at the height of

z, the radiation emitted from an atmospheric layer with the depth of dz is,

(1)\mathrm{\Delta }R(z)=k(z)\rho (z)B(T(z))\mathrm{d}z,

In Eq. (1), B (T(z)) is the Planck function, k(z) is the absorption coefficient of atmospheric gas composition, ρ(z) is the atmospheric gas concentration, and the contribution of the layer dz to the total radiation from the top atmosphere is

(2)R=\mathrm{\Delta }R(z)e^{-{\int }_z^{\infty }k(z\prime )\rho (z\prime )dz\prime }=B(T(Z))d\tau (z),

In Eq. (2),

(3)\tau (z)=e^{-{\int }_z^{\infty }k(z\prime )\rho (z\prime )dz\prime },

is the atmospheric transmittance over the height z. Thus, the total radiation observed by the satellite detector is

(4)R=ϵB(T(\mathrm{0}))\tau (\mathrm{0})+{\displaystyle {\int }_{\mathrm{0}}^{\infty }k(z)\rho (z)B(T(z))\tau (z)d}z,

where, ϵ refers to the surface emissivity. The absorption coefficient of the atmospheric gas composition can be calculated from absorption spectrum line data sets (e.g., AFGL or HITRAN databases). Given the atmospheric temperature profile, the atmospheric concentration of absorptive gases can be obtained using the nonlinear atmospheric radiation transfer equation as expressed in Eq. (4). In the neighborhood of the estimated initial concentration in the atmosphere, the first-order variation to Eq. (4) is,

(5)\delta R={\displaystyle {\int }_{\mathrm{0}}^{\infty }k({\rho }_{\mathrm{0}}(z\prime ))\delta \rho (z\prime )d}z\prime ,

Eq. (5) is the first kind linear Fredholm integral equation. To settle linear remote sensing equation, a series of reasonable physical inversion methods were used, primarily including restrictive linear inversion, optimal weight function and iterative methods.

Because the vertical distribution of CH₄ is relatively homogeneous, it can be assumed that the vertical variation of CH₄ is basically constant. Eq. (5) can then be inversely settled as Eq. (6) (Zeng, 1974; Liou, 1991; Wallace and Hobbs, 2006),

(6)\delta \rho ={\displaystyle \frac{\delta R}{{\displaystyle {\int }_{\mathrm{0}}^{z}K({\rho }_{\mathrm{0}}(z\prime ))dz\prime }}}.

Sensitivity studies

For the forward modeling of thermal infrared radiation transfer in the atmosphere, the primary computing methods include the line-by-line integral method, belt model, and k-distribution method. The line-by-line integral method refers to compute transmittance by estimating the contribution of each atmospheric gas to the absorptive spectrum line by line, which allows it to address atmospheric radiation transfer problems (i.e., atmospheric non-uniform paths and overlapping absorption) effectively. As a result, the LBLRTM can be used to forward model thermal infrared outgoing radiation in the atmosphere.

The main features of LBLRTM<FootNote>

http://rtweb.aer.com/lblrtm.html

</FootNote> are as follows (Yang et al., 2002; Mao and Kawa, 2004; Ye et al., 2011):

(1) The Voigt profile is used for absorption line shapes including both collision-broadening and Doppler-broadening processes in the entire atmospheric column.

(2) The continuous absorption model MT CKD (Mlawer, Tobin, Clough, Kneizys, Davies) is employed combining both self-broadening and outer-broadening.

(3) The HITRAN database is used as input.

(4) LBLRTM is an accurate, efficient, and well-validated line-by-line model that is broadly used in atmospheric radiation and remote sensing to validate band models. Based on comparisons of parameters between observated and simulated, the precision can reach 0.5%.

(5) Transmittance, optical depth, degree of attenuation, emittance and Irradiance can be calculated.

In the computing simulation, the U.S. standard atmosphere is employed and assuming the reference to surface emissivity is set to be 0.98, the boundary temperature is 288.2 K and the spectral resolution is 0.025 cm^-1.

Spectral resolution

The spectral resolution should be improved to provide available information in each observed spectrum. With increasing in high signal-to-noise ratios and spectral, manufacturing technology in remote sensor with higher resolution will be required. However, the improvement of spectral resolution will double the cost of satellite production. Consequently, the tradeoff between higher signal-to-noise ratio and the spectral resolution was always considered in the processes of its practical manufacture. On the other hand, a large amount of data with the potential information redundancy and long period for the data analysis should also be considered if spectral resolution is high. Therefore, the selection of the optimal spectral resolution to obtain the necessary and relevant information is important.

By modeling different spectral resolutions in CH₄ absorptive bands, the optimal spectral resolution is obtained to determine the CH₄ spectral features. Figure 2 shows the radiance obtained using three different magnitudes of spectral resolution, from 0.003 to 0.25 cm^-1, in the 1320-1360 cm^-1 band. Within the narrower spectrum, many absorptive valleys contain information about the CH₄ concentration at different heights in the atmosphere. Comparing with the spectral resolutions of 0.25 cm^-1 and 0.003 cm^-1, many weaker absorptive valleys cannot be distinguished from the 0.25 cm^-1 spectral resolution. Therefore, the linear change in the absorptive line with stronger absorption and wider spectrum cannot be captured well. Comparing with the spectral resolutions of 0.025 cm^-1 and 0.003 cm^-1, the position of the absorptive valley or intensity reflects the absorption spectrum characteristics essentially. From the view of qualitative analysis, a spectral resolution of 0.025 cm^-1 reflects well the absorptive spectral characteristics. The following results are all obtained using this resolution specific to the wave-number range of 1320-1360 cm^-1.

CH₄ initial profile

Because information about the CH₄ in this spectrum is limited, it is impossible to extract all vertical distribution information of this target gas. Additionally, almost all the vertical distribution information for inverting the target gas still depends on the initial information in the input profile, which limits the inversion result. Figure 3 shows the change in the top atmospheric outgoing radiance: when the CH₄ mixing ratio increases by 1%, the corresponding change in mean radiance is 0.774%.

Figure 4 shows the change in the outgoing radiance in the chosen inversion band when the atmospheric CH₄ mixing ratio at each layer increases by 0.1 ppmv (from an initial value of the U.S. standard atmosphere). Because the increasing CH₄ concentration will reduce the atmospheric transmittance, the radiance exiting the top of the atmosphere will decrease with increasing CH4 concentration. However, the radiance is greater than that in the U.S. standard atmosphere from 20 to 50 km, where there is significant temperature inversion. As observed in Fig. 4, the overall influence of the CH₄ mixing ratio inversion error is below 0.05%, which is significantly lower than that change in CH₄ change (1%). The change in the top atmospheric outgoing radiance is less than 0.01% of the values in the lower troposphere (0-2 km) and the approximately tropopause (15 km above earth surface), these results indicate that the effect of atmospheric CH4 concentration from 2 to 15 km mainly contribute to the top atmospheric outgoing radiance. The effects of CH4 concentration above 55 km is negligible. Moreover, the change in the top atmospheric outgoing radiance is less than 0.001% from 24 to 32.5 km probably because of the chemical reaction of CH₄.

Temperature dependence

The atmospheric temperature profile determines the Planck thermal radiation of each layer of the atmosphere and thus affects the inversion precision of the atmospheric composition profile. To understand the contribution of the change in atmospheric temperature to the radiance of the top atmosphere, a 1K temperature error is added to each layer of the U.S. standard atmosphere. Figure 5 shows the radiance change after the 1K error is introduced in the temperature profile. As observed in Fig. 5, the curve shape is similar to the δ function. The overall influence of the temperature inversion error is less than the change caused by increasing the CH₄ mixing ratio by 1%. In the lower troposphere (0-2 km), the radiance sensitivity increases. The sensitivity begins to decrease from 2 to 100 km. In detail, the change in the top atmospheric outgoing radiance is less than 0.1% over 7 km; the sensitivity is less than 0.01% over 14 km and almost constant over 60 km, indicating that the change in the top atmospheric outgoing radiance is mainly caused by the atmospheric temperature changing in the troposphere.

Water-vapor interference

Water vapor is absorbed throughout almost the entire 0-15000 cm^-1 band which includes the near infrared solar radiation and nearly the entire infrared region (Ho et al., 2002). Furthermore, spatial and temporal variability in water-vapor were observed by height in the tropospheric atmosphere. As shown in Fig. 1, water-vapor has lower absorption values compared to the values in CH₄ in the 1320-1360 cm^-1 band. A 10% increase in water-vapor is added to each layer of the U.S. standard atmosphere. Figure 6 shows the radiance change after the 10% error is introduced into the water-vapor profile. The height of the peak position is 3 km, and the sensitivity is 0.3273%, which is much smaller than that with a 1% CH₄ change. The sensitivity is less than 0.1% in the nearer ground layer and over 8 km. Knowledge of these features is highly advantageous when it removes majority of the water-vapor influence in the column CH₄ inversion. Thus, the water-vapor profile must be known with high precision to separate the contribution of the atmospheric column density variation from the signal due to changes in the atmospheric CH₄ mixing ratio.

Interference of N₂O, CO₂, O₃, CO

As shown in Fig. 1, N₂O, CO₂, O₃, and CO has low absorption in this solar infrared band. As listed in Table 1, compared with the U.S. standard atmosphere, the influence of inversion errors of 3× the N₂O concentration and 5× the CO₂ concentration are 0.4219% and 0.4452%, respectively, which are much smaller than the change due to an increase in CH₄ concentration by 1%. The interference of O₃ in this band is much smaller; even the influence of 10× the O₃ concentration (0.0038%) is far less than that of a 1% increase in the CH₄ mixing ratio. The radiance sensitivity is still 0, even for an increase of 10× the CO content. Thus, no absorbtion were observed in CO in this inversion band. The differences in CH₄ sensitivity with and without the above mentioned greenhouse gases are negligible in our calculations for most lines. Therefore, the minor interference by the variable atmosphere contents of N₂O, CO₂, O₃, and CO is a great advantage of this solar infrared band in comparison with other CH₄ bands.

Surface albedo

Surface albedo refers to the ratio of reflected radiation flux density of solar radiation on the surface to the total incident radiation flux concentration, which is also an important factor for atmospheric gas inversion. For surface albedo values of 0.01, 0.02, 0.03, 0.04, 0.05, as shown in Table 2, the larger the surface albedo, the smaller change in the radiance in the top atmosphere. Furthermore, the corresponding change in radiance will be smaller when the CH₄ mixing ratio increases by 1%. Additionally, the change in the CH₄ content is increasingly small for the same radiation change, but the change is not obvious. However, the overall radiance change is less than that caused by an increase of 1% in the mixing ratio of CH4 specified in the U.S. standard atmosphere.

Our results show that the interference of N₂O, CO₂, O₃, and CO was minor in this solar infrared band overall (Table 1). Minor interference from the variable atmospheric water-vapor content is a great merit of this solar infrared band compared with other CH₄ solar bands (i.e., 2.3 μm and 3.3 μm bands), the change in radiance because of the sensitive factors (i.e., CH4 initial profile, temperature, overlapping gases, and surface albedo) is less than that caused by an increase in the CH₄ mixing ratio by 1% in the U.S. standard atmosphere.

Conclusions

Based on a 0.025 cm^-1 spectral resolution and the use of LBLRTM as a forward model of atmospheric radiation transfer, a series of sensitivity studies have been performed to explore the influence of the CH₄ initial profile, temperature, overlapping gases and surface albedo on the inversion precision of atmospheric CH₄ column density. The results indicate that a relatively small CH₄ variation may be detected in the radiance measurement of reflected solar infrared radiation at 7.6 μm.

The interference of N₂O, CO₂, O₃, and CO was minor in this solar infrared band overall. Our full radiative transfer calculations show that the difference in CH₄ sensitivity with and without water-vapor is negligible for most layers. Therefore, minor interference from the variable atmospheric water-vapor content is a great merit of this solar infrared band in comparison with other CH₄ solar bands (i.e., 2.3 μm and 3.3 μm bands). Meanwhile, an accurate atmospheric temperature profile is required as ancillary data for the CH₄ inversion. The recently launched global atmospheric temperature profilers should meet this requirement. Additionally, the atmospheric column concentration is needed for the analysis of CH₄ concentration. It can be diminished their influences on the inversion precision in the inversion real atmospheric CH₄ column concentrations only by considering the factors mentioned above and controlling their precision.

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